Gayle Woodford's body was found in a shallow roadside grave. Photo: Facebook

A Mimili man, 36, who was arrested and charged with vehicle theft on Thursday after police stopped a local ambulance normally driven by Ms Woodford near Coober Pedy, was then charged with murder on Sunday.

Another man and a woman who were also in the ambulance have not been charged.

Forensic investigators spent Sunday making their way to the site where Ms Woodford's body was found.

The death of the 56-year-old nurse has shocked the tight-knit remote healthcare community.

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She had worked for the Nganampa Health Council for more than five years.

The council's medical director Paul Torzillo told ABC Ms Woodford was held in high regard and his organisation was focusing on supporting her husband, family and colleagues.

"Gayle was a loved, incredibly popular and extremely competent nurse with our organisation for a long period of time," he said.

Remote healthcare association CRANAplus executive officer Christopher Cliffe told AAP many people in the industry were "very angry and upset" over Ms Woodford's disappearance and death.

"Even if you didn't know Gayle herself, you know people who know her, it's a very small group of highly skilled health professionals and it's tightly knit, it's such a horrific tragedy to occur," he said.

Mr Cliffe said while it was too early to know the exact circumstances surrounding Ms Woodford's death, there had been safety concerns for remote healthcare workers for some time.

He said the vulnerability of clinicians needed to be recognised and workers should not be allowed to work at posts alone to ease the stress of isolation and workload.

A change.org petition has also been started calling for the abolition of single nurse posts, with more than 12,000 supporters by Sunday evening.

Following the discovery of the body on Saturday afternoon, Superintendent Des Bray told reporters the "worst fears were realised".

"Gayle, I'm told, was a much loved person here, so this is devastating news not just for Fregon but for the whole APY community," he said.